Subnational Inequality in Latin America: Empirical and Theoretical Implications of Moving beyond Interpersonal Inequality

Abstract

In many countries around the world, living in one subnational unit versus another can be just as important as race or class as a determinant of differential access to opportunities and wellbeing. Despite this fact, scholars still heavily emphasize interpersonal income inequality. This article develops and implements new tools to shift from interpersonal to subnational inequality and from economic to social inequality. It develops a novel concept and measurement of subnational social inequality that overcomes the inconsistencies between definitions and measurements found in existing research on the subject. Focusing on Latin America, the article applies the new measurement tools to reveal differences in the evolution and rankings of interpersonal and subnational forms of inequality. Such findings challenge our existing knowledge of both the levels and the sources of inequality in the region. To make sense of these discoveries, the article suggests that the usual drivers of interpersonal inequality—such as neoliberal reforms and authoritarianism—might drive down subnational inequality, while well-known inequality fighters—such as democratization and left party rule—might not be as effective at combating its subnational variety.

Appendix

Inequality Measurements of Gap and Dispersion

Gap Measurements

• a) Range

Definition: The range provides the difference between the highest and the lowest value on a variable. When used in subnational analysis, it provides the full extent of variation of an attribute across spatial units. If subnational illiteracy rates go from 5 to 25, the range would be 20.

Advantages: It captures the idea of the gap between the better-off and the worse-off areas, it is easy to compute and simple to understand.

Disadvantages: The range is not commonly used as an inequality measurement because it does not comply with the inequality axioms, or a group of desirable properties that inequality measurements should respect. There are four axioms: the transfers principle, the scale invariance principle, the translation invariance principle, and decomposability.¹⁰ As the range only takes into account two units and it depends on the scale, it does not fulfill any of the axioms. However, the axioms for inequality measurements were mainly developed for the study of individual income inequality, and they are not necessarily suited for subnational inequality in social development indicators. In fact, and as was shown in the text with the examples of countries A and B, complying with the scale invariance axiom obscures the existence of subnational inequality.

• b) Ratios

Definition: The ratio is computed by dividing the highest value by the lowest value, or values set at different percentiles.

Advantages: Ratios can be used in cross-country and cross-attribute comparisons.

Disadvantages: As the ratio complies with the scale invariance principle, it does not allow us to tap the gap dimension of subnational inequality that makes a difference between country A and country B, in the text’s example. For this reason, the range is better suited than the ratio for our concept of subnational inequality.

• c) Beta Convergence (B.C)

Definition: Economists study subnational inequality by using sigma and beta convergence. Sigma convergence is the coefficient of variation, while beta convergence refers to the relationship between the initial level of an attribute and its growth rate over a time period. B.C takes place when the worse-off regions improve faster than the better-off regions, lessening the range. Theoretically, B.C refers to the idea that when the worse-off catch up there is reduction in inequality. B.C is measured by running a lineal regression in which the growth rate of an indicator in each subnational unit in a previously established period of time is the dependent variable, and the initial level acts as the independent variable. If the coefficient (b) is negative, there is beta convergence (Barro and Sala-i-Martin 1992).

Disadvantages: It is possible that the worse-off grows so fast that it overcomes the better off, producing more inequality instead of reducing it. The measurement of B.C would suggest a reduction in inequality when an increment in inequality is taking place (Gyuris 2014: 213). Additionally, beta convergence describes whether inequality is increasing or decreasing, but gives no information on the extent of such inequality. Lastly, the fact that the time frame for which B.C is calculated must be predetermined raises suspicions, since the criteria for selecting the time period are not clear and often different time frames give different results. To sum up, B.C, although commonly used by economists, does not fulfill a few desirable attributes of a subnational inequality measurement.

Dispersion Measurements

• a) Standard Deviation and Coefficient of Variation.

Definition: The standard deviation provides an idea of the dispersion of an attribute around the mean. If the values of a given variable are very spread out, the standard deviation is high. When applied to spatial analysis it would tell, on average, how distant from the mean are the values of the different spatial units. The standard deviation can be weighted by population size. The weighted standard deviation acknowledges that each spatial unit has a different population size, reducing the impact of depopulated and outlier provinces in the distribution.

Disadvantages: The standard deviation, however, says little if not placed in the context of the mean. For example, the dispersion of a variable in a dataset with standard deviation of 3 looks very different if the mean is 5 or 500. If the mean is 5, the data is very dispersed. If the mean is 500, the data is not dispersed at all.

The coefficient of variation—our selected measurement for dispersion—is the solution to this problem because it is computed by dividing the standard deviation by the mean. It can also be weighted by the population size of each subnational unit. Additionally, it is independent of the unit in which the variable is measured. In every case, the higher the C.V, the greater the dispersion of a given attribute. The (weighted) C.V is as apt for inequality measurement as the Gini coefficient.

• b) Spatial Gini

Definition: The Gini Coefficient is a measure of dispersion because it measures the extent to which the distribution of an attribute among individuals or groups deviates from a perfectly equal distribution. It is defined in two main ways: as the average difference in an attribute between all pairs of individuals or groups or as the area between the Lorenz curve and the egalitarian line by the area of the egalitarian triangle. The Gini can be used for groups and individuals. When applied to spatial analysis, each spatial unit is considered to be a group with a population weight. The Gini captures whether the amount of an attribute possessed by each group is proportional to its size. It ranges from 0 where all subnational units have the same access, to 1 where there is absolute concentration of an attribute in one subnational unit.

Advantages: The Gini is probably the most commonly used measurement of inequality. It is scale invariant and sensitive to transfers.

Disadvantages: However, the Gini is used for continuous variables that are cumulative in nature, such as income or years of schooling. It is not commonly used for categorical (e.g., race), discrete (e.g., educational attainment), or bounded variables (e.g. illiteracy or infant mortality rates (Thomas et al. 2001). This is reflected in the fact that a Gini of a rate—for instance, illiteracy—is completely different from the Gini of its opposite—literacy.

• c) Theil Index

Definition: The Theil Index is a measure of dispersion that allows decomposition in between group and within group inequality. If disaggregate data is available, the Theil index would tell how much inequality corresponds to the differences between groups and the differences between individuals.

Disadvantages: Despite being very appropriate for spatial analysis due to its decomposable nature, the Theil Index suffers from a major shortcoming: it is sensitive to population size, which means that it is not comparable across countries with different numbers of subnational units (Elbers et al. 2008). In addition, the Theil Index is difficult to understand and compute and is not intuitive.